Each side of an equilateral triangle is incre | vedclass

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(C) Let the original side of the equilateral triangle be $a$.The original area $A = \frac{\sqrt{3}}{4} a^2$.The new side length $a' = a + 1.5\% 	ext{

Vedclass · Accepted Answer

$3.0225$

Vedclass · Answer

(C) Let the original side of the equilateral triangle be $a$.The original area $A = \frac{\sqrt{3}}{4} a^2$.The new side length $a' = a + 1.5\% 	ext{ of } a = a(1 + 0.015) = 1.015a$.The new area $A' = \frac{\sqrt{3}}{4} (a')^2 = \frac{\sqrt{3}}{4} (1.015a)^2 = \frac{\sqrt{3}}{4} a^2 (1.015)^2$.Since $A' = A 	imes (1.015)^2$,we calculate $(1.015)^2 = 1.030225$.So,$A' = 1.030225 A$.The percentage increase in area $= \frac{A' - A}{A} 	imes 100 = (1.030225 - 1) 	imes 100 = 0.030225 	imes 100 = 3.0225 \%.$

Each side of an equilateral triangle is increased by $1.5 \%$. The percentage increase in its area is......$\%$

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